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How network theory predicts the value of Bitcoin

Metcalfe’s Law, which measures the value of a network, can calculate a cryptocurrency’s value—and predict when to get out.

Philosophers, economists, and theorists have various ways to judge how money should be valued. Some have said that its worth lies in a high cost of production. Others see it as simply a form of credit that allows the transfer of resources, which is why it can take the form of pieces of paper or even digital records.

Then there is the idea that a currency is worth whatever somebody is willing to pay for it given the limited supply. This explains the extraordinary valuations sometimes seen for the cryptocurrency Bitcoin.

All these approaches run into trouble of one form or another. There is certainly a high cost of production in the cryptographic “proof of work” required to create, or mine, bitcoins. But their value has little relation to this cost. By the end of 2017, a single Bitcoin was worth almost $20,000, and the cryptocurrency market as a whole had a value of $830 billion. Just a few weeks later, the market had collapsed to $280 billion.

So how much is a Bitcoin really worth?

Today we get an answer of sorts, thanks to the work of Spencer Wheatley at ETH Zurich in Switzerland and a few colleagues, who say the key measure of value for cryptocurrencies is the network of people who use them. What’s more, they say, once Bitcoin is valued in this way it becomes possible to see when it is overvalued and perhaps even to spot the telltale signs that a market crash is imminent.

The value of a network is famously accredited to Bob Metcalfe, the inventor of Ethernet and founder of the computer networking company 3Com. Metcalfe’s Law states that a network’s value is proportional to the square of the number of its users.

It’s straightforward to calculate a value for Bitcoin based on the number of active users. Wheatley and co fit the data to a generalized Metcalfe’s Law that allows them to tweak the parameters, arriving at an exponent of 1.69 rather than Metcalfe’s original square of the number of users (i.e., an exponent of 2).

This makes sense. The original law is based on the idea that the value of a network grows in proportion with the number of all possible connections. In other words, it assumes that all nodes can connect with each other.

“This does not seem realistic,” say Wheatley and co. Their finding is that each user is on average linked to N2/3 other users. “For instance, for N = 1 million, a typical user is then connected to ‘only’ 10,000 other users, a more realistic figure,” they say.

With these parameters, the generalized Metcalfe’s Law more accurately reflects the way Bitcoin’s value has increased with the number of users.

It also reveals when Bitcoin has been overvalued. Wheatley and co point to four occasions when Bitcoin has become overvalued and then crashed; in other words, when the bubble has burst.

These events have been well documented. The first big crash occurred in 2011 when Mt. Gox, a major Bitcoin exchange in Tokyo, was hacked, presaging an 88 percent drop in the cryptocurrency’s value over the next three months.

A crash in 2012 was preceded by the discovery of a Ponzi fraud involving Bitcoin. Another crash occurred in 2013 when high trading volumes overwhelmed Mt. Gox, causing it to collapse; the value of Bitcoin then dropped by 50 percent in two days.

The most recent collapse, at the end of 2017, occurred after South Korean regulators threatened to shut down cryptocurrency exchanges.

To study these collapses, Wheatley and co use a model developed by Didier Sornette, who is the professor of entrepreneurial risks at ETH Zurich and one of this paper’s authors. Sornette has long suggested that it is possible to predict the collapse of speculative bubbles using certain characteristics of the markets. Indeed, readers of this blog will be familiar with his ideas.

Sornette’s approach has two components. First, he looks for markets that are growing at a super-exponential rate—in other words, markets where the growth rate itself is growing.

That can happen for short periods of time because of factors such as herding behavior. But it is not sustainable without an infinite number of people. For this reason, a crash, or correction, is inevitable.

This much is uncontroversial. But Sornette goes on to say that the timing of the crash is predictable. That’s because the unsustainable growth rates leads to huge volatility. And this makes the market increasingly unstable, to the point that almost any small disturbance can trigger a crash.

So in the Bitcoin crashes listed above, the triggering events are insignificant. According to Sornette, the market was already in a critical phase, and if these events hadn’t occurred, some other event would have triggered a crash instead.

The situation is analogous to a forest fire. If the forest is dry enough to burn, almost any spark can trigger a blaze. And the size of the resulting fire is unrelated to the size of the spark that started it. Instead, it is the network of connections between the trees that allows the fire to spread.

The controversy over Sornette’s work is how accurately he can make these predictions. Clearly, a prediction that Bitcoin is about to crash in the next few hours or days is much more powerful than a prediction that it will crash in the coming months or years.

Nevertheless, the researchers say it allows them to predict market crashes using data from the past and so should allow them to spot similar imminent crashes in the future. They put it, rather confusingly, like this: “[Our] model is shown to provide an ex-ante warning of market instabilities, quantifying a high crash hazard and probabilistic bracket of the crash time consistent with the actual corrections; although, as always, the precise time and trigger (which straw breaks the camel’s back) being exogenous and unpredictable.”

According to the generalized Metcalfe’s Law, Bitcoin is significantly overvalued, even after the crash at the end of 2017. “Our Metcalfe-based analysis indicates current support levels for the bitcoin market in the range of 22–44 billion USD, at least four times less than the current level,” they say.

And that means there is uncertain weather ahead, at best. Wheatley and co compare the current Bitcoin market conditions to those following the collapse of the Mt. Gox trading system. “The current market resembles that of early 2014, which was followed by a year of sideways and downward movement,” they say.

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